It does say specifically (or it used to) that WP's are not wizards.
With some creative cheese cutting we might get WP's that can cast multiple RIP spells and not cancel the old ones. 
This is clearly against the spirit and intent of the rules.
Warhammer Basic Rule Book pg. 110
"
Some spells...clearly marked as 'remains in play'...lasts until the Wizard chooses to end it, attempts to cast another spell."
Clearly these are the rules that pertain to spells tagged with 'remains in play'. All prayers that last multiple turns are clearly marked as Remains in Play.
While pg. 110 provides the provisio that the RIP spells may contain exceptions, it also says any exceptions will be
specified in the spell's description or
other special rules.
Nothing on pg. 52 or 53 of the NEB contains anything resembling such exceptions. In fact, the book specifies on pg. 53 that
"Prayers are cast exactly like bound spells".
Going back to the basic rule book and the section on bound spells, it clearly states "
The spell...is cast in the players magic phase just like other spells (for example, it cannot be cast by fleeing models) and it can be countered in the same way as ordinary spells".
Clearly the intent here is that bound spells operate exactly like normal spells with the exception that you don't roll power dice and the dispel score is set at the power level.
Also, you may
NOT have an Archlector recast an RIP prayer on his second prayer if your opponent dispelled it on the first go. You
MUST cast a different prayer if you want to pray again. The relevant passage is as follows "An ArchLector may use two
different prayers per turn..."
The word
use is different than the words successfully cast, or not dispelled. You use a prayer and your opponent is given his chance to dispell it. Regardless of whether he succeeds or even attempts to dispel the prayer, you have already used it up and must wait until your next magic phase before trying again.